1 · Adding three-digit numbers
Line up the ones, tens, and hundreds. Add the ones first. If a column makes 10 or more, write the ones digit and carry the 1 to the next column.
367 + 218: ones 7 + 8 = 15, write 5, carry 1. Tens 6 + 1 + 1 = 8. Hundreds 3 + 2 = 5. Answer: 585.
2 · Subtracting with regrouping
When the top digit is smaller, borrow from the next column: one ten becomes ten ones.
524 − 337: ones 4 − 7 will not work, so borrow: 14 − 7 = 7. Tens 1 − 3 will not work, borrow again: 11 − 3 = 8. Hundreds 4 − 3 = 1. Answer: 187.
Always check by adding back: 187 + 337 = 524. ✓
3 · Make a hundred
Adding is easiest when a pair makes a round number. In 79 + 15 + 85, spot that 15 + 85 = 100. Then 79 + 100 = 179. No carrying at all.
Look for pairs whose ones digits add to 10: 72 + 64 + 28 + 36 → (72 + 28) + (64 + 36) = 100 + 100 = 200.
4 · Compensation: round, then fix
To add 99, add 100 and take 1 back: 264 + 99 = 364 − 1 = 363. To subtract 98, subtract 100 and give 2 back: 531 − 98 = 431 + 2 = 433.
The move: change a number to a round one, do the easy sum, then undo the change.
5 · Use a problem you already solved
You know 757 − 492 = 265. What is 757 − 494? You took away 2 more, so the answer is 2 less: 263.
And 759 − 492? You started with 2 more, so the answer is 2 more: 267. Never restart from scratch when a neighbor is already done.
6 · Compare without computing
Which is greater, 311 − 151 or 311 − 115? Both start at 311. The one that takes away less leaves more: 115 < 151, so 311 − 115 is greater.
For sums the rule flips: 208 + 181 > 208 + 118 because you add more. Read the digits; do not add.
7 · Parentheses first
37 − (10 + 7) means "do the bracket first": 37 − 17 = 20. Without the bracket, 37 − 10 + 7 goes left to right: 27 + 7 = 34. Same numbers, different answers.
A useful family: 58 − 21 − 13 is the same as 58 − (21 + 13). Taking away two amounts one after the other is the same as taking away their total.
8 · Find the missing digit
1▢8 + 213 = 401. Work backwards: 401 − 213 = 188, so the box is 8. Or reason column by column: 8 + 3 = 11, carry 1; the tens must make 0 with a carry, so ▢ + 1 + 1 = 10, ▢ = 8.
Either way, check: 188 + 213 = 401. ✓
9 · Missing numbers in equations
x + 35 = 72. The two sides balance. Take 35 off both sides: x = 72 − 35 = 37.
54 − x = 23 asks "54 take away what leaves 23?" That is 54 − 23 = 31. Check: 54 − 31 = 23. ✓
10 · More than, fewer than: one step at a time
A hamster has 67 grains. 12 are rice. There are 7 more corn than rice, and 4 fewer buckwheat than corn. The rest are quinoa.
Corn: 12 + 7 = 19. Buckwheat: 19 − 4 = 15. Rice + corn + buckwheat = 46. Quinoa: 67 − 46 = 21. Write each answer down before the next step.
11 · Estimate to the nearest hundred
For "about how much," round each number to the nearest hundred, then add. 397 + 512 is about 400 + 500 = 900.
On the number line, 397 sits just below 400, so it rounds up; 512 sits just above 500, so it rounds down. A quick estimate also catches silly mistakes: if you got 1,909, something went wrong.
12 · Reach the next round number
173 + ▢ = 200. Count up: 173 → 180 is 7, 180 → 200 is 20. So ▢ = 27. This is also how you make change and how you subtract in your head: 200 − 173 = 27.
Counting up to a round number turns hard subtraction into easy addition. You are ready for the test! 🎉
Ready to practice?
Take the free 24-question test. It starts easy and builds to harder, ISEE-style reasoning. It's auto-scored, and you can review every answer afterward.